“I ended up finding one 10 minutes before the shop closed,” the ballroom pro, 26, told PEOPLE of his day-long hunt around London for the old-school accessory required for the horse race.

Ballas had been invited to Saturday’s event – for which men are also required to wear tails or “morning jackets” – by former Dancing partner (and season runner-up) Katherine Jenkins, the Welsh opera star who sang the British national anthem for the Queen and the 130,000-strong crowd.

“Katherine said nothing will ever compare to the nerves of Dancing with the Stars,” Ballas says. And having been raised in England himself (from age 3 to 21, he lived in Liverpool and then London), Ballas never broke a sweat around her majesty, either.

“I was just standing there, jaw-dropped,” he says of sipping champagne a mere six feet away from the Queen (and other members of the Royal Family, including Princesses Beatrice and Eugenie) on the exclusive Paddock. Though royal protocol dictates “You never speak unless spoken to,” Queen Elizabeth did introduce herself to Jenkins, “who did a little curtsy,” Ballas says.

In person, the monarch is “tiny and very extravagant, lovely and gorgeous,” he says. “She looked amazing.”

Katherine Jenkins and Mark BallasCourtesy of Mark BallasAnd as “honored” as he was to celebrate her 60-year reign in classic royal style, he couldn’t help but observe, “She’s just a super cute grandma!”